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Question

Life saver rating for step by step complete answer. Thank you

A sinusoidal transverse wave moves along a stretched string in the + direction with amplitude 5.00 cm, wavelength 2.00 m. and wave speed 200 m/s. The particles in the string oscillate along the z axis. What are the wave number, frequency and angular frequency of the wave? Write a possible wave function for the wave with an explanation. If the tension in the string is 50.0 N, what is the linear mass density of the string? How much average power is transmitted along the string? What would the wave function be in (b) if the wave traveled in the - direction?

Explanation / Answer

a)

wave number = k = 2/ = 2*3.14/2 = 3.14 m-1

frequency = f = k v = 3.1416*200 = 628.32 628 Hz

angular frequency = = 2 f = 2*3.1416*628.32 = 3948 rad/s

b)

z(y,t) = A sin(ky - t) = 0.05 sin(3.14 y - 3948 t)

c)

v = (T/)

= T/v2 = 50/(200*200) = 0.00125 Kg/m

d)

P = (1/2) A2 2 v = 0.5*0.00125*(0.05*0.05)*(3948*3948)*200

e)

z(y,t) = A sin(ky + t) = 0.05 sin(3.14 y + 3948 t)

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